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Special valuations and automorphisms of affine log Calabi--Yau varieties
Yuchen Liu
Let be an affine log Calabi--Yau variety. Although special and finitely generated valuations are defined using a log CY-Fano compactification of , we prove that the correspo…
Relative stability theory and properness of K-moduli spaces
Harold Blum, Yuchen Liu, Chenyang Xu +1
We define the relative stability threshold of a family of Fano varieties over a DVR and show that it is computed by a divisorial valuation. In the case when the special fiber is K-…
Irreducible symplectic varieties with a large second Betti number
Yuchen Liu, Zhiyu Liu, Chenyang Xu
We prove a general result on the existence of irreducible symplectic compactifications of non-compact Lagrangian fibrations. As an application, we show that the relative Jacobian f…
A note on Kollár valuations
Yuchen Liu, Chenyang Xu
We prove the set of Kollár valuations in the dual complex of a klt singularity with a fixed complement is path connected. We also classify the case when the dual complex is one dim…